I have a very specific question regarding peer review. We recently submitted our work to a well-known journal and received a fast peer review decision. One reviewer said that our paper was missing an important component, and cited our work to support their claim. They requested us to use the approach presented in our previous paper. This paper, however, was written by me. This make me believe the reviewer does not know my identity. Their comment does not make sense (they are clearly not familiar with the topic). Is it inappropriate to say "We did this like that back then but now we found a more optimal method"? Unlike here (In single-blind peer-review, can you reveal your identity without the editor's consent?), I am not a reviewer but the author.
No, you should not do that. The articles published by that journal become somewhat trustworthy because there is a quality control procedure in place that articles have to go through. Part of that is double blind review. It is the journal's decision when to deviate from that procedure, not yours.
Moreover that should not be necessary. You have substantive arguments for your choice, so present those. That is a more valid form of argument than "believe me because I am the author".
Regardless, the reviewers don't decide, the editor does, and the editor knows who everybody is.
Think about the reviewer's comment on its merits. It points to previous work in the area that they think should be cited. The fact that it's yours is irrelevant.
The reviewer is representative of your eventual readers. If the reviewer is confused there's a problem with the paper. Perhaps you need to revise it to refer to that earlier work and explain why it's not relevant in this one.
If you think that's really unnecessary, then respond to the editor explaining why you are rejecting the reviewer's suggestion.
Speculation about whether the reviewer knows you wrote the other paper is irrelevant.
This comes down to "does the journal you submitted to practice double-blind peer review?". You should know this, because if the answer is yes, you probably rewrote your paper to anonymize it.
If you didn't rewrite your paper (and since you seem surprised that the reviewer does not know who you are) I would assume the journal does not conduct double-blind peer review, in which case yeah, go ahead and tell them the method they suggest does not work as well.